Instruction 14-6
a Local Store Developed a Multiplicative Time-Series Model $$\log _ { 10 } \hat { Y } = 6.102 + 0.012 X - 0.129 Q _ { 1 } - 0.054 Q _ { 2 } + 0.098 Q _ { 3 }$$

question 81

Multiple Choice

Instruction 14-6
A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the four-year period from 2005 to 2009. The following is the resulting regression equation:
$$\log _ { 10 } \hat { Y } = 6.102 + 0.012 X - 0.129 Q _ { 1 } - 0.054 Q _ { 2 } + 0.098 Q _ { 3 }$$
Where
$X$ is the coded quarterly value with $X = 0$ in the first quarter of 2005 .
$Q _ { 1 }$ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
$Q _ { 2 }$ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
$Q _ { 3 }$ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Instruction 14-6,in testing the significance of the coefficient for Q₁ in the regression equation (-0.129) which has a p-value of 0.492,which of the following is the best interpretation of this result?

• A) The revenues in the first quarter of the year are significantly different than the revenues in the fourth quarter (\(\alpha\) = 0.05).
• B) The revenues in the first quarter of the year are not significantly different than the revenues in the fourth quarter (\(\alpha\)= 0.05).
• C) The revenues in the first quarter of the year are significantly different than the revenues in an average quarter (\(\alpha\) = 0.05).
• D) The revenues in the first quarter of the year are not significantly different than the revenues in an average quarter (\(\alpha\) = 0.05).

---

Definitions:

Basilar Membrane

A key structure in the cochlea of the inner ear that plays a crucial role in the mechanical process that converts sound waves into nerve impulses.

Hair Cells

Tiny sensory cells found in the inner ear that translate sound vibrations into neural signals.

Auditory Nerve

The nerve that transmits sound information from the inner ear to the brain.

Eardrum

A thin, tightly stretched membrane located in the middle ear that vibrates in response to sound waves, aiding in the transmission of sound to the inner ear structures.